I'm far from sure about the grammatical details, but using the nominative in this case makes it seem like a statement about the speaker. "Wir sind gute Hoffnung" would be akin something like "Wir sind gute Fußballer" or "Wir sind neue Mitglieder im Verein".

But the phrase doesn't mean that we are hope, rather that we have hope. Maybe (though that's just a guess on my part) it's a shortened version of something like "Wir sind in guter Hoffnung".

As a general phrase, "Ich bin guter Hoffnung, dass..." means something like you're hoping and optimistic that something will turn out positively and as planned. An example would be "Ich bin guter Hoffnung, dass wir in den Verhandlungen zu einer Einigung kommen werden".

Used on its own the meaning is more specific. "Wir sind guter Hoffnung" means that you (or your partner) are pregnant. That version is commonly used in plural, similar to the English "we are pregnant" or "we are expecting (a child)".

Both version, extended with a clause and own its own, are considered relatively outdated in todays German. Using them wouldn't necessarily give a negative impression, but it would make you appear somewhat quaint.

Thanks for the clarification, but curious about your last comment, @Henning-Kockerbeck would you really need the plural? Like in English we have the phrase "We are the last hope" type phrase where we can be a singular thing (hope rather than hope). Must it be plural in German?

I'm not sure as well. This is a fixed expression for being pregnant. It can be genitive or dative. I always thought it being a partitive usage of genitive meaning we have some good hope. In older literature there are many examples for this usage. Sie tranken viel guten Weines (plenty of). Now having had a closer look on it I rather think that it is an instrumental usage of genitive which
is also quite elaborate but a little bit more common nowadays. So it would mean something like "we are carrying;with". In this sense I would understand it even in not idiomatic expressions. Guter Hoffnung stiegen wir in die Höhle (with best expectations we entered the cove). Other examples of that usage. Guten Gewissens kann ich dem nicht zustimmen. Langsamen Schrittes näherte er sich. Sehenden Auges rannte er in sein Verderben. Most of these examples would be expressed with dative (and mit) in a more up to date version. Mit gutem Gewissen kann ich dem nicht zustimmen. Mit langsamem Schritt (or better, mit langsamen Schritten) näherte er sich.

I've never heard being pregnant in plural, even in cases like "All of my friends are expecting a baby" Alle meine Freunde sind guter Hoffnung.

I meant to say, if "Hoffnung" were nominative, we'd need the plural, "Wir sind gute Hoffnungen". Maybe a different example illustrates the point better: You wouldn't say "Wir sind Kind" ("We are child"), but "Wir sind Kinder" ("We are children").

If you add an additional article, you can combine plural and singular, just like in English: "Wir sind ein Verein" ("We are a club").